Average Error: 0.0 → 0.0
Time: 6.4s
Precision: 64
\[\sqrt{1 - x \cdot x}\]
↓
\[\sqrt[3]{\left(1 - x \cdot x\right) \cdot \sqrt{1 - x \cdot x}}\]
\sqrt{1 - x \cdot x}
↓
\sqrt[3]{\left(1 - x \cdot x\right) \cdot \sqrt{1 - x \cdot x}}
double f(double x) {
        double r5225152 = 1.0;
        double r5225153 = x;
        double r5225154 = r5225153 * r5225153;
        double r5225155 = r5225152 - r5225154;
        double r5225156 = sqrt(r5225155);
        return r5225156;
}
↓
double f(double x) {
        double r5225157 = 1.0;
        double r5225158 = x;
        double r5225159 = r5225158 * r5225158;
        double r5225160 = r5225157 - r5225159;
        double r5225161 = sqrt(r5225160);
        double r5225162 = r5225160 * r5225161;
        double r5225163 = cbrt(r5225162);
        return r5225163;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\sqrt{1 - x \cdot x}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\sqrt{1 - x \cdot x} \cdot \sqrt{1 - x \cdot x}\right) \cdot \sqrt{1 - x \cdot x}}}\]

  4. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{\left(1 - x \cdot x\right) \cdot \sqrt{1 - x \cdot x}}}\]

  5. Final simplification0.0

    \[\leadsto \sqrt[3]{\left(1 - x \cdot x\right) \cdot \sqrt{1 - x \cdot x}}\]

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))